If you like nitpicking around C code and generated assembly language — and we’ll admit that we do — you shouldn’t miss [Scaramanga’s] analysis of what’s known as Kernighan’s trick. If you haven’t heard of the trick, it’s a pretty efficient way of counting bits.
Like the Wheatstone bridge and a lot of other things, the Kernighan trick is misnamed. Brian Kernighan made it famous, but it was actually first published in 1960 and again in 1964 before he wrote about it in 1988. The naive way to count bits would be to scan through each bit position noting how many one bits you encounter, but the problem is, that takes a loop for each bit. A 64-bit word, then, takes 64 loops no matter what it contains. You can do slightly better by removing each bit you find and stopping when the word goes to zero, but that still could take 64 cycles if the last bit you test is set.